Question

Joe and Matt are volunteering to collect canned goods for the local food bank. They each recorded the total number of cans collected and their time spent volunteering on graphs. Match the correct equation that represents each of their graphs.
the first graph goes from 0 to 5 10
# of cans collected
10
098765
1
y
Joe's Collection Rate
0 1 2 3 4 5 6 7 8 9 10
Hours
X

the second goes from 0 to 3 10
# of cans collected
10
9
Matt's Collection Rate
87654+ 3
2
0 1 2 3 4 5 6 7 8 9 10
Hours
X

y=3x
y=x
y=4x
y=2x

Answer 1

I can't read the graphs clearly from the text you pasted — could you upload the images or tell me one clear point from each line (for example "at 5 hours Joe had 10 cans" or "at 3 hours Matt had 9 cans")?

How to match quickly: each equation is a constant rate (slope) = cans ÷ hours.
- If the line goes through (0,0) and (5,10), slope = 10/5 = 2 → y = 2x.
- If it goes through (0,0) and (3,9), slope = 9/3 = 3 → y = 3x.
- If it goes through (0,0) and (3,3), slope = 3/3 = 1 → y = x.
- If it goes through (0,0) and (3,12), slope = 12/3 = 4 → y = 4x.

From your text I can confidently say Joe = y = 2x (5 hours → 10 cans). Tell me one point on Matt's line (or upload the graph) and I'll pick the correct equation for him.